Robust dynamic average consensus algorithm for signals with bounded derivatives

TLDR: Development and analysis of a robust dynamic average consensus algorithm for arbitrary reference signals with known bounded derivatives is presented and a singularly perturbed system is introduced that would effectively place an integral between the consecutive Laplacian matrices.

Abstract: Development and analysis of a robust dynamic average consensus algorithm for arbitrary reference signals with known bounded derivatives is presented. The proposed approach does not rely on full knowledge of the dynamics generating the reference signals nor assume access to its time derivatives. Compared to existing approaches, the proposed algorithm does not require any initialization criteria and therefore it is robust to changes in network topology. Robustness of the proposed approach is attributed to the two consecutive Laplacian matrices that appear in the algorithm and thus two rounds of communication are needed between each update of the agents' estimates. Therefore we introduce a singularly perturbed system that would effectively place an integral between the consecutive Laplacian matrices and allow the nodes to replace the two rounds of communication involving a single variable with a single round of communication involving two variables. Numerical simulations validate the theoretical contributions of the paper.